Was flipping through the New York Times Magazine’s annual Year in Ideas issue, which included the idea of the “Designated Hitter as Moral Hazard”, which presented John-Charles Bradbury and Doug Drinen’s analysis that the introduction of a DH increased the chances of a hit-by-pitch. (Here’s their paper: “Moral Hazard on the Mound - the Economics of Plunking”. Edit: this is the updated version.) This seems to make intuitive sense - no chances to retaliate when the pitcher doesn’t bat - but as far as I recalled the HBP rates of both leagues are actually not that different. From tangotiger’s posts in an old Baseball Primer discussion on the topic, the HBP rates are:
1955-1972: AL .0057, NL .0055
1973-2003, AL .0065, NL .0060
Which is to say, the AL does seem to have 10% more HBPs, but .0065 HBPs per plate appearance translates into a very small number of total HBPs. It also indicates that the AL has historically had a higher HBP rate than the NL, so I’m not sure that the DH coefficient in the findings is measuring some other difference in the leagues. It’s true that you can do a comparison between pre- and post-DH AL stats to isolate the effects of the DH from other league differences, but the authors only, unfortunately, have access to two non-DH AL years, 1969 which is as they note a problematic year for stats given the post-1968 changes introduced, and 1972.
What I think is quite interesting is Figure 1 of their paper, which shows that generally the AL had more HBPs over the NL starting in the 1970s even pre-DH, an advantage which rose in the 1980s and then fell in the 1990s and 2000s. This seems to suggest that HBP rates might be influenced more strongly by factors other than the introduction of the DH: off the top of my head, for example, the introduction of body armour taking out the “cost” of a HBP to a batter (which would also explain why both leagues showed a marked increase in HBPs from the mid-1980s onwards), and the standardisation of both leagues’ umpires and strike zones.
I guess while I think that Bradbury and Drinen’s work adds a lot of insight into the economics of baseball, particularly in their use of play-by-play analysis, the fact that the differences in HBP between leagues already existed before the DH rule and only seemed to markedly increased in 1980 makes me a bit skeptical about whether the positive DH coefficient is masking something else. (Thinking out loud, new rules preventing retaliation were introduced by MLB in 1978. Could that have led somehow to an increase in the difference in HBP rates between the AL and the NL in the 1980s?)
Also, if one league’s umpires were more likely than the other to toss pitchers for retaliation within a game, this might create differences in the HBP rates. That also brings in the concept of next-game retaliation - sometimes, the game situation doesn’t allow for a retaliation, and the ’traditional’ thinking is that the next time the two teams face off, a retaliation pitch might take place. Perhaps there needs to be a dummy variable for ‘unretaliated pitches’. Incidentally, Gregory Trandel (in “Hit by Pitches: Moral Hazard, Cost-Benefit, Retaliation, or Lack of Evidence?”) notes that there’s no correlation in total HBPs experienced by any team’s batters and its pitchers per season, for what it’s worth.
Also, I wonder about brushback pitches. If a pitcher has good control, he doesn’t necessarily need a HBP to retaliate - but how does one quantify that fact?
Intuitively, another way to confirm the results would be to look at the effect of DH introduction into other baseball leagues, but I’m not sure how good minor league historical stats (or Japanese stats, which might be interesting given that they also have the ‘one league has a DH, one doesn’t’ situation) are for this kind of analysis. The magazine article did note that the findings from interleague seemed to confirm the idea that NL pitchers were more likely to hit players in DH games and AL pitchers were less likely in games where pitchers had to bat, so there seems to be further evidence of the moral hazard argument - I’m leaning towards accepting that it exists, but I’m not fully convinced yet, so I’d be interested in seeing those findings.
That’s my admittedly scattershot musings on the topic. Maybe when I have time to sit down and think about it I might have more coherence to the ideas here…
Incidentally, since we’re talking about the Year in Ideas, how about Glenn Stout’s research showing that there were anti-Semitic roots to the idea that the Red Sox are cursed? One of the best articles written in ESPN this year.